Shape Preserving Mesh Simplification

1. A computer-implemented method for mesh simplification of a three-dimensional polygon mesh, the method comprising: identifying, by one or more computing devices, a structural edge in the three-dimensional polygon mesh using plane detection; constructing, by the one or more computing devices, a sharp edge in the three-dimensional polygon mesh at the structural edge, the sharp edge comprising a straight chain of connected vertices in the three-dimensional polygon mesh; identifying, by the one or more computing devices, a candidate edge for edge collapse, the candidate edge being associated with a first vertex and a second vertex; determining, by the one or more computing devices, an error for collapsing the candidate edge to a new vertex, the error determined such that the new vertex is located on the sharp edge; and collapsing, by the one or more computing devices, one or more edges in the three-dimensional polygon mesh based at least in part on the error; wherein when the first vertex is located on the sharp edge and the second vertex is not located on the sharp edge, determining an error for collapsing the candidate edge to a new vertex comprises determining the error such that the new vertex is located at the first vertex.

2. The computer-implemented method of claim 1 , wherein the sharp edge is associated with a curved structural feature.

3. The computer-implemented method of claim 2 , wherein the sharp edge for the curved structural feature is constructed as a chain of sharp edges.

4. The computer-implemented method of claim 1 , wherein constructing, by the one or more computing devices, the sharp edge in the three-dimensional polygon mesh at the structural edge, comprises: identifying, by the one or more computing devices, an edge segment to be constructed at a detected plane intersection between a first detected plane and a second detected plane; identifying, by the one or more computing devices, a set of vertices for the edge segment, the set of vertices comprising one vertex from each of the first detected plane and the second detected plane closest to an end of the edge segment; determining, by the one or more computing devices, a closing path for the edge segment based at least in part on the set of vertices; and modifying, by the one or more computing devices, the three-dimensional polygon mesh based on the closing path.

5. The computer-implemented method of claim 4 , wherein modifying, by the one or more computing devices, the three-dimensional mesh based on the closing path comprises: removing, by the one or more computing devices, a portion of the three-dimensional polygon mesh within the closing path; and constructing, by the one or more computing devices, the sharp edge along the edge segment in the three-dimensional polygon mesh.

6. The computer-implemented method of claim 1 , wherein the method comprises filtering, by the one or more computing devices, the sharp edge based on one or more of length of the sharp edge, height of the sharp edge, or areas of planes corresponding to the sharp edge.

7. The computer-implemented method of claim 1 , wherein when the first vertex is located on the sharp edge and the second vertex is located on a different sharp edge, determining an error for collapsing the candidate edge to a new vertex comprises computing the error such that the candidate edge is not collapsible.

8. The computer-implemented method of claim 1 , wherein the error is a quadrics error.

9. The computer-implemented method of claim 1 , wherein the three-dimensional polygon mesh provides a representation of a cityscape.

10. The computer-implemented method of claim 9 , wherein the sharp edge is representative of a building edge in the representation of the cityscape.

11. A computer program product comprising a tangible non-transitory computer-readable medium storing computer-readable instructions for execution by one or more processors, causing the one or more processors to perform operations, the operations comprising: identifying a structural edge in the three-dimensional polygon mesh representative of a geographic area using plane detection; constructing a sharp edge in the three-dimensional polygon mesh at a detected plane intersection associated with the structural edge, the sharp edge comprising a straight chain of connected vertices in the three-dimensional polygon mesh; identifying a candidate edge for edge collapse, the candidate edge being associated with a first vertex and a second vertex; determining an error for collapsing the candidate edge to a new vertex, the error determined such that the new vertex is located on the sharp edge; and collapsing one or more edges in the three-dimensional polygon mesh based at least in part on the error; wherein the operation of constructing the sharp edge in the three-dimensional polygon mesh at the structural edge, comprises: identifying an edge segment to be constructed at a detected plane intersection between a first detected plane and a second detected plane; identifying a set of vertices for the edge segment, the set of vertices comprising one vertex from each of the first detected plane and the second detected plane closest to an end of the edge segment; determining a closing path for the edge segment based at least in part on the set of vertices; and modifying the three-dimensional polygon mesh based on the closing path.

12. The computer-program product of claim 11 , wherein the operation of modifying the three-dimensional mesh based on the closing path for each edge segment to construct the sharp edge comprises: removing portions of the three-dimensional polygon mesh within the closing path; and constructing the sharp edge along the edge segment in the three-dimensional polygon mesh.

13. A computer-implemented method for mesh simplification of a three-dimensional polygon mesh, the method comprising: identifying, by one or more computing devices, a structural edge in the three-dimensional polygon mesh using plane detection; constructing, by the one or more computing devices, a sharp edge in the three-dimensional polygon mesh at the structural edge, the sharp edge comprising a straight chain of connected vertices in the three-dimensional polygon mesh; identifying, by the one or more computing devices, a candidate edge for edge collapse, the candidate edge being associated with a first vertex and a second vertex; determining, by the one or more computing devices, an error for collapsing the candidate edge to a new vertex, the error determined such that the new vertex is located on the sharp edge; and collapsing, by the one or more computing devices, one or more edges in the three-dimensional polygon mesh based at least in part on the error; wherein when the first vertex is located on the sharp edge and the second vertex is located on a different sharp edge, determining an error for collapsing the candidate edge to a new vertex comprises computing the error such that the candidate edge is not collapsible.